A particle of mass m is driven by a machine that delivers a constant power k watts. If the partilcle starts from rest the force on the particle at time t is

A particle of mass m is driven by a machine that delivers a constant p

1.	A particle of mass m is driven by a machine that delivers a constant power k watts. If the partilcle starts from rest the force on the particle at time t is
Answer» <P>`sqrt(2 MK) t^(-1//2)` `1/2 sqrt(mk) t^(-1//2)` `sqrt((mk)/(2)) t^(-1//2)` `sqrt(mk) t^(-1//2)` Solution :Constant power acting on the particle of mass m is k watt. or `P = k or (dW)/(DT) = k, dW = kdt` INTEGRATING both sides, `int_0^W dW = int_0^t k dt` `IMPLIES W = kt` Using work energy theorem, `W = 1/2 mv^2 - 1/2 m(0)^2` `kt = 1/2 mv^2 " or " v = sqrt((2kt)/(m))` Acceleration of the particle, `a = (dv)/(dt) = 1/2 sqrt((2k)/(m) = 1/(sqrtT)) = sqrt((k)/(2mt))` Force on the particle , `F = ma = sqrt((mk)/(2t)) = sqrt((mk)/(2)) t^(-1//2)`.